The k-ary n-dimensional shuffle-exchange directed network S(k, n) consists of kn nodes such that each node is represented as an k-ary n-tuple vector, a1a2···an, where ai is in [0, k-1]. Node a1a2···an is adjacent to node a2a3···ana1 (one shuffle link) and k-1 other nodes a1a2···an-1b, where b∈[0, k-1] and b≠an (k-1 exchange links). S(k, n) have been widely used as topologies for VLSI networks, parallel architectures, and communication systems. However, since S(k, n) does not exist for the number of nodes between kn and kn+1, Liu and Hsu have recently proposed a class of digraphs GS(k, N), which generalized S(k, n) to any number N of nodes. They also showed that GS(k, N) retains all the nice properties of S(k, n). In this paper, we survey these combinatorial properties and study Hamiltonian properties of GS(k, N). In particular, we have successfully obtained Hamiltonian circuit for GS(k, k(k+1)) for any k>2.
|Original language||English (US)|
|Journal||Proceedings - IEEE International Symposium on Circuits and Systems|
|State||Published - Jan 1 1999|
|Event||Proceedings of the 1999 IEEE International Symposium on Circuits and Systems, ISCAS '99 - Orlando, FL, USA|
Duration: May 30 1999 → Jun 2 1999
ASJC Scopus subject areas
- Electrical and Electronic Engineering